I like trying to figure out what the heck Kant is trying to say, so here's another idea about his infamous principle...

In logic, in some way or other, there's a distinction between categorical and hypothetical sentences. On the assumption that this is a distinction of reason, then if there can be imperatives of either form, it follows that categorical imperatives exist at a minimum as natural formulae in imperative logic.

Now, the concept of "substance" is often parsed as "a subject that cannot objectively be a predicate of something else," e.g. although, "Red is a color," can be switched around in words as, "A color is red," or whatever, in the objects themselves there are some things relations that can't be flipped around like this. Kant's picture of logic traces the concept of substance to the form of categorical judgments in general, so in imperative logic, a categorical imperative refers to something that cannot objectively be a practical predicate. But that is only to speak of that which cannot be a means to other ends only, but must be an end in itself. So, the concept of an end-in-itself as such follows from the mere form of practical judgment, and denying that there are categorical imperatives to be explained in such terms, would amount to refusing to use a certain part of formal logic (or asserting that the use of it was irrational).

EDIT: Which, I suspect is pointless: denying that imperative argument/logic exists would be to deny the referential function of all language whatsoever, since each unit of a language refers through an implicit mental imperative, from the signifier to the signified.